Uniform Robot Relocation Is Hard in only Two Directions Even Without Obstacles
Given n robots contained within a square grid surrounded by four walls, we ask the question of whether it is possible to move a particular robot a to a particular grid location b by performing a sequence of global step operations in which all robots move one grid step in the same cardinal direction (if not blocked by a wall or other blocked robots). We show this problem is NP-complete when restricted to just two directions (south and west). This answers the simplest fundamental problem in uniform global unit tilt swarm robotics.
Caballero, D., Cantu, A.A., Gomez, T., Luchsinger, A., Schweller, R., Wylie, T. (2023). Uniform Robot Relocation Is Hard in only Two Directions Even Without Obstacles. In: Genova, D., Kari, J. (eds) Unconventional Computation and Natural Computation. UCNC 2023. Lecture Notes in Computer Science, vol 14003. Springer, Cham. https://doi.org/10.1007/978-3-031-34034-5_2
UCNC 2023. Lecture Notes in Computer Science, vol 14003